Question

On your ninth birthday, you received $300 which you invested at 5 percent interest, compounded annually. Your investment is now worth $756. How old are you today?

Answer 1

So it will take 20 years to accumulate 300 to 756, so present age will be 29 years.

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FV = PV (1 + r)^n

Where,

Future value (FV) = $756

Present value (PV) = $300

Rate of interest (i) = 0.05

We need to find the value of (n)

Let's put all the values in the formula,

756 = 300 (1 + 0.05) ^n

756/ 300 = (1.05) ^n

2.52 = (1.05) ^n

To solve this equation we need to apply log on both sides, so the equation will be

log (2.52) = log (1.05) ^n

We know that log (m)^n = n* log (m)

log (2.52) = n log (1.05)

Values of log can be found in the log table, or we can use calculator, so let's put the values of logs

0.401400540781544 = n * 0.0211892990699381

n = 0.401400540781544/ 0.0211892990699381

n = 18.94355

So the value of n is 18.94 years

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Hope this answer your query.

Feel free to comment if you need further assistance. J